2 Marks Questions

Question 12 Marks

Rahul scores $80$ marks in English and $x$ marks in Hindi. What is his total score in the two subject$?$

Answer

Marks obtained in English $= 80$
Marks obtained in hindi $= x$
Total marks obtained $= 80 + x$

Question 22 Marks

One pencil costs $Rs. 2$ and one fountain pen costs $Rs. 15.$ What is the cost of $x$ pencils and $y$ fountain pens$?$

Answer

Cost of one pencil $= Rs. 2$
Cost of $x$ pencils $= Rs. 2x$
Cost of one fountain pen $= Rs. 15$
Cost of $y$ fountain pens $= Rs. 15y$
Total cost of $x$ pencils and $y$ fountain pens $= Rs. (2x + 15y)$

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Question 32 Marks

Think of a number. Multiply it by $5.$ Add $6$ to the result. Subtract $y$ from this result. What is the result?

Answer

Let the number be $x.$ On multiplying the number by $5,$ we get: $5x$ Further, adding $6$ to $5x,$ we get: $5x + 6$ Finally, on subtracting y from $5x + 6,$ we get: $5x + 6 - y$

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Question 42 Marks

The number of rooms on the ground floor of a building is $12$ less than the twice of the number of rooms on first floor. If the first floor has $x$ rooms, how many rooms does the ground floor has?

Answer

Let the number of rooms on the ground floor be $y.$ It is given that the number of rooms on the first floor is $x;$ therefore, we have: $y = 2 \times x - 12 = 2x - 12$ Thus, the number of rooms on the ground floor is $2x - 12.$

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Question 52 Marks

The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two-third of its breadth. Find its area if its breadth is $x \ cm.$

Answer

Breadth of the given rectangle $= x \ cm.$
Length of the rectangle $=\frac{2}{3}\text{x cm}$
$\therefore$ Area of rectangle $=\frac{2}{3}\text{x}\times\text{x}=\frac{2}{3}\text{x}^2\ \text{cm}^2$

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Question 62 Marks

The number of bacteria in a culture is $x$ now. If becomes square of itself after one week. What will be its number after two weeks?

Answer

Present number of bacteria in a culture $= x$
Number of bacteria in the culture after one week $= x^2$
Number of bacteria in the culture after two weeks $= (x^2)^2= x^4$

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Question 72 Marks

Write down $7 x y^2 \times 3 x^2 y \times 5 y^4$ in the exponential form.

Answer

$7 x y^2 \times 3 x^2 y \times 5 y^4$
$=(7 \times 3 \times 5) \times\left(x \times x^2\right) \times\left(y^2 \times y \times y^4\right)$
$=105 x^3 y^7$

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Question 82 Marks

One apple weighs $75$ grams and one orange weighs $40$ grams. Determine the weight of $x$ apples and $y$ oranges.

Answer

Weight of an apply $= 75$ grams.
Weight of an orange $= 40$ grams.
Weight of $x$ apples $= 75 \times x = 75x$ grams.
Weight of $y$ oranges $= 40 \times y = 40y$ grams.
Total weight of $x$ apples and $y$ oranges $= (75x + 40y)$ grams.

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